The “fold” has its equal in the german “fach” which means x*n of the n-fold. The “times” is just a synonymous term that developed too.

I think you might get confused here, because it is usually used in the context of something having increased tenfold, which us often used to describe the result of an exponential growth. Nobody says “it increased twofold”. Outside of scientific topics, language doesnt really refer to exponential growth. As we saw with Covid, it is a concept difficult to grasp for people in general and it is not part of the day to day language.